Texture On Plane Issue?
The video texture doesn't need to continuously run in the background, as blender draws or renders a frame where the texture is visible it will read the one relevant frame from the video that it needs, this is similar to it reading any other image textures in your scene. As you are using a small video it will most likely be cached in RAM while it is being used and have little impact on performance.

To prevent your fire from always being visible you can animate the visibility of your plane both in the viewport and the render.